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navik [9.2K]
3 years ago
10

The standard formula for the volume of a cone is V=πr2h3. If the cone is scaled proportionally by a factor of k, its volume beco

mes V' = V × k3. Use your algebra skills to derive the steps that lead from V=πr2h3to V' = V × k3 for a scaled cone.

Mathematics
2 answers:
DaniilM [7]3 years ago
8 0

The volume of a cone with base radius <em>r </em>and height <em>h</em> is

V = \frac 1 3 \pi r^2 h

What happens when we scale by <em>k </em>?

Let <em>V'</em> be the volume of a cone with radius <em>rk</em> and height <em>hk</em>

V' = \frac 1 3 \pi (rk)^2 (hk) = \frac 1 3 \pi r^2 k^2 h k = k^3 (\frac 1 3 \pi r^2 h) = k^3 V

ANEK [815]3 years ago
3 0

Answer:

Step-by-step explanation:

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3 years ago
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Ashley mixes two types of soft drinks with different types of concentration: one soft drink has 20% sugar and the other drink ha
ICE Princess25 [194]

Answer:

Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

<em></em>

Step-by-step explanation:

Sugar concentration of first drink = 20%

Volume of first soda = 250 ml

Sugar in first soda = 20% of 250 ...... (1)

Sugar concentration of second drink = 45%

Volume of second soda = 250 ml

Sugar in second soda = 45% of 250 ...... (2)

Let x\% be the sugar concentration in resultant mixture.

Volume of mixture = 250 + 250 = 500 ml

Sugar in mixture = x\% of 500 ml ...... (3)

Total sugar concentration (Adding (1) and (2)) and equating it to equation (3):

20% of 250 + 45% of 250 = x\% of 500

\Rightarrow \dfrac{20}{100} \times 250 + \dfrac{45}{100} \times 250 =  \dfrac{x}{100} \times 500\\\Rightarrow 2 \times x = 65\\\Rightarrow x = 32.5\%

Hence, Sugar concentration of the mixed soft drink will be <em>32.5%.</em>

8 0
2 years ago
(1, 4) is a solution to the system that includes y=3x + 1 and y = -x + 5.
SIZIF [17.4K]

Answer:

yes

Step-by-step explanation:

y=3x + 1

y = -x+5

Check if (1,4) solves the first equation

4 = 3(1)+1

4 = 3+1

4=4

This is true

Check the second equation

4 = -1+5

4=4

This is true

(1,4) is a solution to the system of equations

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padilas [110]
The answer is B.

Breaking down the operation:

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Denumerators: x × x = x² and +2 × -2 = -4

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\frac{x+3}{x+2} × \frac{x-3}{x-2}

Hope it helped,

Happy homework/ study/ exam!

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3 years ago
What's 7x + 14 + 2x + 3 = 2 ( x + 26 ). Show work
Blababa [14]
Do you mean (x=26)? If so, 7 times 26 + 14 +2 times 26 + 3 = 2... i dont know...
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